How to win a penalty shootout

At the end of this february the two english soccer teams Chelsea Football Club and Liverpool Football club play each other in a well known final for the domestic English Football cup. The game was filled with immense action full of missed opportunities, incredible saves and multiple offsides. The game due to this continued into overtime as both teams were unable to finish their chances and put the game away. After two additional 15 minute halves of overtime the game was to be decided by a penalty shootout. Chelsea here made an interesting decision. Their Goalkeeper Eduard Mendy, was subbed out in a tactical move, being replaced by a penalty kick specialist known as Kepa Arrizabalaga. However, this did not go Chealsea’s way as on the 11th kick Kepa missed his penalty saving zero in total losing the shootout and the cup. Mendy was superb during this game, he was mentally locked in, making incredible saves and arguably up to that point was man of the match. So did Chealsea make the right decision?

Kepa had been quite successful previously to this shootout, where chelsea had not lost a shootout he had been in this year. He had dealt with the pressure in larger games such as the European super cup where he ended up saving 2 penalties becoming the hero single handedly winning his side the cup. However it did not favor him this time. It can be difficult to save a penalty, as there are many aspects and variables that are involved in saving a penalty such as determining the dominant foot the kicker will use, searching out and predicting based on bodily signs such as the direction of running, eyes staring to a particular corner or the shape of their hips. It can become a mental duel between the person at the spot and the person taking the kick. With all this said the question to still be determined was Should have Kepa been on the field.

When assessing Kepa’s stats he has faced within league matches a total of 23 penalties saving 7 and conceding 17. This comes out to a save percentage of 41%. This in comparison to Eduard Mendy’s 2 saves out of 32 faced penalties is far superior. Kepa more than quadruples Mendy’s pathetic save percentage of 6%. By this alone an argument could be made that it was not Kepa’s day, however he should have been the man on the field at that time. However, there are many undiscussed variables, one of which being the state that Mendy was in. He was in top form ending the game with double digit saves and ended the match with the highest player rating of an 8.5. One thing that can play a major effect within Penalty kicks is nerves. This can lead to world class players blowing kicks they have struck a million times. Some things that play into this pressure in the forms of an intimidation factor is the record, form and physical stature of the keeper. In the model below it illustrates P2 as Chelsea with the two choices of fielding Kepa or keeping Mendy, with Liverpool responding having 4 choices of feeling pressure or no pressure (calmness) with both keepers. When mathematically analyzed it is shown that it was the right decision to field Kepa as it was more likely that the outcome that would come from him would be a victory.

Although this is a simplified way of thinking when it comes to shootouts, the deep economics and mathematics involved within it are nothing short of complex. Based on the environment, the day the vibe the manager is feeling can trump the stats or initial plan that was created days or weeks in advance. From this we can never judge a manager’s decision as the odds sometimes are everchanging .

t(M)HP S1: 3(.8)+-3(.2) and -3(.8)+3(.2)
HP S1:(1.6,-1.8)
HP S2:3(.6)+.4(-3)


S2(-.1.2, .6)


For P1
EU of HP:

EU of P:


Use Kepa when the probability of them being calm with him is less than 66%


Use Mendy when the probability is more than 33%

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